Homeomorphisms of the 3-sphere that preserve a Heegaard splitting of genus two

Author:

Cho Sangbum

Abstract

Let H 2 {\mathcal H_2} be the group of isotopy classes of orientation-preserving homeomorphisms of S 3 \mathbb S^3 that preserve a Heegaard splitting of genus two. In this paper, we construct a tree in the barycentric subdivision of the disk complex of a handlebody of the splitting to obtain a finite presentation of H 2 {\mathcal H_2} .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference8 articles.

1. E. Akbas, A presentation for the automorphisms of the 3-sphere that preserve a genus two Heegaard splitting, preprint, 2005, ArXiv:math.GT/0504519.

2. L. Goeritz, Die Abbildungen der Berzelfläche und der Volbrezel vom Gesschlect 2, Abh. Math. Sem. Univ. Hamburg 9 (1933), 244-259.

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5. Virtually geometrically finite mapping class groups of 3-manifolds;McCullough, Darryl;J. Differential Geom.,1991

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